1997/01/30 by Takashi Dateki, T. Dateki · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #High-Energy Particle Collisions Research #Quantum Chromodynamics and Particle Interactions #hep-th
paper · pdf · doi:10.1143/ptp.97.921
published as Prog.Theor.Phys. 97 (1997) 921-938 · 22 pages, 15 Postscript Figures, LaTeX
arxiv created 1997/01/30 · openalex publication_date 1997/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
We study the critical behavior of theD(2<D<4)-dimensional Gross-Neveu model with a Thirring interaction, where a vector-vector type four-fermi interaction is on equal terms with a scalar-scalar type interaction. By using an inversion method up to the next-to-leading order of the 1/N expansion, we construct a gauge invariant effective potential. We show the existence of the chiral order phase transition, and determine explicitly the critical surface. It is observed that the critical behavior is mainly controlled by the Gross-Neveu couplingg. The critical surface can be divided into two parts by the surfaceg=1, which is the critical coupling in the Gross-Neveu model at the 1/N next-to-leading order, and the form of the critical surface is drastically change atg=1. Comparison with the Schwinger-Dyson (SD) equation is also discussed. Our result is almost the same as that derived in the SD equation. In particular, in the case of the pure Gross-Neveu model, we succeed in deriving exactly the same critical line as that derived in the SD equation.